Space of modular forms of level 1323, weight 4, and Character 1323.bl

• Label: 1323.4.bl
• Level: $1323$
• Weight: $4$
• Character orbit: 1323.bl
• Rep. character: $\chi_{1323}(100,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $1992$
• Sturm bound: $672$

Defining parameters

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1323.bl (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 441 \)
Character field:			\(\Q(\zeta_{21})\)
Sturm bound:			\(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1323, [\chi])\).

	Total	New	Old
Modular forms	6120	2040	4080
Cusp forms	5976	1992	3984
Eisenstein series	144	48	96

Trace form

1992 * q + 8 * q^2 + 648 * q^4 + 45 * q^5 + 4 * q^8 - 10 * q^10 + 5 * q^11 + 7 * q^13 + 278 * q^14 + 2544 * q^16 - 134 * q^17 - 72 * q^19 - 355 * q^20 + 11 * q^22 - 205 * q^23 - 7905 * q^25 - 238 * q^26 + 144 * q^28 + 341 * q^29 - 54 * q^31 - 386 * q^32 - 13 * q^34 + 317 * q^35 - 1118 * q^37 + 1417 * q^38 - 43 * q^40 - 685 * q^41 + 79 * q^43 - 479 * q^44 - 3286 * q^46 - 74 * q^47 + 270 * q^49 + 9 * q^50 + 667 * q^52 - 1850 * q^53 - 1300 * q^55 + 7721 * q^56 - 1297 * q^58 - 1658 * q^59 + 5434 * q^61 + 1896 * q^62 - 19332 * q^64 - 634 * q^65 - 288 * q^67 - 20086 * q^68 + 1037 * q^70 + 2890 * q^71 + 310 * q^73 - 411 * q^74 - 1461 * q^76 - 2902 * q^77 + 342 * q^79 + 10877 * q^80 - 34 * q^82 - 1153 * q^83 - 130 * q^85 + 4713 * q^86 + 731 * q^88 + 2588 * q^89 - 1580 * q^91 + 9853 * q^92 + 1184 * q^94 + 1445 * q^95 + 252 * q^97 - 9027 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1323, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)